^{1}and Ken-ichi Saitow

^{1,2,a)}

### Abstract

Vibrational Raman spectra of C=C stretching modes of ethylene derivates (*cis*-C_{2}H_{2}Cl_{2}, *cis*-stilbene, and *trans*-stilbene) were measured in supercritical fluids along an isotherm as functions of their densities. The substitution effect of the Raman shift is so significant that a difference among three solutes can be 20 times and is observed similarly in dipolar (CHF_{3}) and non-dipolar (CO_{2}) fluids. In particular, the shifts of *trans*-stilbene were enormously large among all systems for studies of vibrational spectroscopies of supercritical fluids and were equivalent to those of typical hydrogen-bonded fluids. Such large shifts arising from the significant attractive energy between solute and solvent molecules were attributed to a site-selective solvation around a phenyl group, which was driven by a dispersion force in the absence of steric hindrance. We found that the absence of steric hindrance causes the significant local density augmentation. To the best of our knowledge, Raman experiments and their theoretical analysis are the first ones quantifying how the difference of steric hindrance produces solvation structures in solution as well as supercritical solutions.

K.S. acknowledges the “Structure Control and Function” of PRESTO of the Japan Science and Technology Agency (JST) for substantially supporting this research. This study was also supported by a Grant-in-Aid for Young Scientists (B) (13740321) and Young Scientists (A) (16685001) from the Ministry of Education, Science and Culture of Japan and by the Sumitomo Foundation Award for Young Researchers.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Solvents
- 22.0
- Supercritical fluids
- 21.0
- Raman spectra
- 12.0
- Dispersion
- 9.0
- Carbon dioxide
- 7.0

## Figures

Vibrational frequency shifts measured in all supercritical fluid systems at *ρ* _{r} = 0.7. Left column: solute, measured band, and solvent. Cited references and measured temperatures are listed in Table I. Str: stretching mode, def: deforming mode, *c*-: *cis*-, *t*-: *trans*-, pNA: *p*-nitroaniline, MeOH: methanol, EtOH: ethanol, and p-ABN: *p*-aminobenzonitrile.

Vibrational frequency shifts measured in all supercritical fluid systems at *ρ* _{r} = 0.7. Left column: solute, measured band, and solvent. Cited references and measured temperatures are listed in Table I. Str: stretching mode, def: deforming mode, *c*-: *cis*-, *t*-: *trans*-, pNA: *p*-nitroaniline, MeOH: methanol, EtOH: ethanol, and p-ABN: *p*-aminobenzonitrile.

Thermodynamic states for Raman spectral measurements on (a)–(f) pressure-temperature and (g)–(l) density-pressure phase diagrams. Solid lines in Figs. (a)-(f) are the liquid-vapor coexistence curves. Solid lines in Figs. (g)–(l) are visual guides obtained by fitting polynomial functions to the data. The term *ρ* _{r} is the reduced density represented by *ρ* _{r} = *ρ*/*ρ* _{c}.

Thermodynamic states for Raman spectral measurements on (a)–(f) pressure-temperature and (g)–(l) density-pressure phase diagrams. Solid lines in Figs. (a)-(f) are the liquid-vapor coexistence curves. Solid lines in Figs. (g)–(l) are visual guides obtained by fitting polynomial functions to the data. The term *ρ* _{r} is the reduced density represented by *ρ* _{r} = *ρ*/*ρ* _{c}.

(a) Typical example of Raman spectra of *trans*-stilbene in supercritical fluid. The band at around 1640 cm^{−1} has been assigned to the C=C stretching mode (see Ref. 5). (b, c) Density dependences of C=C stretching modes of *trans*-stilbene in (b) scCHF_{3} and (c) scCO_{2}. Solid lines are the curve fits using the Lorentzian functions. The term *ρ* _{r} is the reduced density represented by *ρ* _{r} = *ρ*/*ρ* _{c}. In the manuscript, we obtained the peak frequencies of C=C stretching modes by analyzing the spectra using Lorentzian functions.

(a) Typical example of Raman spectra of *trans*-stilbene in supercritical fluid. The band at around 1640 cm^{−1} has been assigned to the C=C stretching mode (see Ref. 5). (b, c) Density dependences of C=C stretching modes of *trans*-stilbene in (b) scCHF_{3} and (c) scCO_{2}. Solid lines are the curve fits using the Lorentzian functions. The term *ρ* _{r} is the reduced density represented by *ρ* _{r} = *ρ*/*ρ* _{c}. In the manuscript, we obtained the peak frequencies of C=C stretching modes by analyzing the spectra using Lorentzian functions.

Frequency shifts of C=C stretching modes of *trans*-stilbene (red), *cis*-stilbene (Ref. 10) (pink), and *cis*-C_{2}H_{2}Cl_{2} (Ref. 11) (black) in scCHF_{3} at *T* _{r} = 1.02. Solid lines are visual guides obtained by fitting polynomial functions to the data.

Frequency shifts of C=C stretching modes of *trans*-stilbene (red), *cis*-stilbene (Ref. 10) (pink), and *cis*-C_{2}H_{2}Cl_{2} (Ref. 11) (black) in scCHF_{3} at *T* _{r} = 1.02. Solid lines are visual guides obtained by fitting polynomial functions to the data.

(a, b) Repulsive (green), net (black), and attractive (red) shifts of C=C stretching modes of *trans*-stilbene in (a) scCHF_{3} and (b) scCO_{2} at *T* _{r} = 1.02. (c, d) Attractive shift of *trans*-stilbene (closed circle), *cis*-stilbene (open circle), and *cis*-C_{2}H_{2}Cl_{2} (+) in (c) scCHF_{3} and (d) scCO_{2}. Solid lines are visual guides obtained by fitting the polynomial functions to the data.

(a, b) Repulsive (green), net (black), and attractive (red) shifts of C=C stretching modes of *trans*-stilbene in (a) scCHF_{3} and (b) scCO_{2} at *T* _{r} = 1.02. (c, d) Attractive shift of *trans*-stilbene (closed circle), *cis*-stilbene (open circle), and *cis*-C_{2}H_{2}Cl_{2} (+) in (c) scCHF_{3} and (d) scCO_{2}. Solid lines are visual guides obtained by fitting the polynomial functions to the data.

(a) The method to obtain the local density augmentation, (*ρ* _{local} − *ρ*)/*ρ* _{c}. Symbols are experimental attractive shifts. Solid line is linear line based on the mean field approximation. (b, c) Local density augmentations of (b) *cis*-stilbene and (c) *trans*-stilbene in scCO_{2}. The quantity of *ρ* _{r} is expressed as *ρ* _{r} = *ρ*/*ρ* _{c}. Solid lines are visual guides obtained by fitting polynomial functions to the data.

(a) The method to obtain the local density augmentation, (*ρ* _{local} − *ρ*)/*ρ* _{c}. Symbols are experimental attractive shifts. Solid line is linear line based on the mean field approximation. (b, c) Local density augmentations of (b) *cis*-stilbene and (c) *trans*-stilbene in scCO_{2}. The quantity of *ρ* _{r} is expressed as *ρ* _{r} = *ρ*/*ρ* _{c}. Solid lines are visual guides obtained by fitting polynomial functions to the data.

Attractive shifts of C=C stretching modes of (a) *trans*-stilbene and (b) *cis*-stilbene (Ref. 10) in scCHF_{3} (blue) and scCO_{2} (red) at *T* _{r} = 1.02.

Attractive shifts of C=C stretching modes of (a) *trans*-stilbene and (b) *cis*-stilbene (Ref. 10) in scCHF_{3} (blue) and scCO_{2} (red) at *T* _{r} = 1.02.

## Tables

Systems, temperatures, and references of the data in Fig. 1. The number in the left column represents the order of the shifted amount at *ρ* _{r} = *ρ*/*ρ* _{c} = 0.7, as shown in Fig. 1.

Systems, temperatures, and references of the data in Fig. 1. The number in the left column represents the order of the shifted amount at *ρ* _{r} = *ρ*/*ρ* _{c} = 0.7, as shown in Fig. 1.

Molecular parameters for calculations of the repulsive shifts.

Molecular parameters for calculations of the repulsive shifts.

Molecular parameters.

Molecular parameters.

Dispersion (dis), dipole-induced-dipole (DID), and dipole-dipole terms in Ref. 44.

Dispersion (dis), dipole-induced-dipole (DID), and dipole-dipole terms in Ref. 44.

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